Tony Pulis' seven-year reign at the Britannia Stadium came to an end on Tuesday night, with the club confirming the termination of the manager's contract by mutual consent.
"We will wait and see who the club decide to bring in," he said. "The chairman is a very sensible man, very level-headed and knows his football and he will definitely bring in the right person for Stoke."
Supporters became disenchanted with poor form and performances in the second half of the season which saw the Potters win just three of 19 league matches and briefly flirt with the prospect of relegation.
But Etherington warned them to be careful what they wished for.
"Fans were grumbling saying they wanted him out or wanted a change but it looks like they have got their wish," he told talkSPORT.
"You have to be careful what you wish for in football sometimes. You look at Charlton under Alan Curbishley and look where they are now (back in the Championship having dropped into League One from being a Premier League team).
"Hopefully it won't go that way for us, hopefully we'll get someone in who will push us on and make us into a top-10 team.
"If you look at where Stoke were when he (Pulis) first came in - mid-table in the Championship - you can't argue he's done a fantastic job.
"He's a great man, a fantastic man. He's done a lot for me personally, a lot for the football club and for the people of Stoke-on-Trent as well."
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